Download Use the Distributive Property to factor each polynomial. 1. 21b − 15a

The greatest common factor in each term is 2j k .
8-5 Using the Distributive Property
Use the Distributive Property to factor each
polynomial.
1. 21b − 15a
Factor each polynomial.
5. np + 2n + 8p + 16
SOLUTION: SOLUTION: The greatest common factor in each term is 3.
6. xy − 7x + 7y − 49
SOLUTION: 2
2. 14c + 2c
SOLUTION: 7. 3bc − 2b − 10 + 15c
The greatest common factor in each term is 2c.
2 2
2
SOLUTION: 2
3. 10g h + 9gh − g h
SOLUTION: 8. 9fg − 45f − 7g + 35
SOLUTION: The greatest common factor in each term is gh.
Solve each equation. Check your solutions.
9. 3k(k + 10) = 0
SOLUTION: 2
2
2 2
4. 12j k + 6j k + 2j k
SOLUTION: Since 0 is on one side of the equation and the other
side is in factor form, apply the Zero Product
Property and set each factor equal to 0. Solve each
of the resulting equations.
3k(k + 10) = 0
The greatest common factor in each term is 2j k .
The roots are 0 and –10. Check by substituting 0 and
–10 in for k in the original equation.
Factor each polynomial.
5. np + 2n + 8p + 16
SOLUTION: eSolutions Manual - Powered by Cognero
6. xy − 7x + 7y − 49
Page 1
SOLUTION: 8-5 Using the Distributive Property
So, the solutions are 0 and –10.
Solve each equation. Check your solutions.
9. 3k(k + 10) = 0
SOLUTION: Since 0 is on one side of the equation and the other
side is in factor form, apply the Zero Product
Property and set each factor equal to 0. Solve each
of the resulting equations.
3k(k + 10) = 0
10. (4m + 2)(3m − 9) = 0
SOLUTION: Since 0 is on one side of the equation and the other
side is in factor form, apply the Zero Product
Property and set each factor equal to 0. Solve each
of the resulting equations.
(4m + 2)(3m − 9) = 0
The roots are 0 and –10. Check by substituting 0 and
–10 in for k in the original equation.
The roots are
and 3. Check by substituting and 3 in for m in the original equation.
So, the solutions are 0 and –10.
10. (4m + 2)(3m − 9) = 0
SOLUTION: Since 0 is on one side of the equation and the other
side is in factor form, apply the Zero Product
Property and set each factor equal to 0. Solve each
of the resulting equations.
So, the solutions are
and 3.
(4m + 2)(3m − 9) = 0
2
11. 20p − 15p = 0
SOLUTION: The roots are
and 3. Check by substituting Since 0 is on one side of the equation, factor the
other side. Next, apply the Zero Product Property
by setting each factor equal to 0. Solve each of the
resulting equations.
and 3 in for m in the original equation.
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The roots are 0 and
Page 2
. Check by substituting 0 and
8-5 Using
Distributive
Property
So, thethe
solutions
are
and 3.
So, the solutions are 0 and
.
2
2
11. 20p − 15p = 0
12. r = 14r
SOLUTION: Since 0 is on one side of the equation, factor the
other side. Next, apply the Zero Product Property
by setting each factor equal to 0. Solve each of the
resulting equations.
SOLUTION: Rewrite the equation so one side has 0 and the other
side is in factor form. Next, apply the Zero Product
Property by setting each factor equal to 0. Solve
each of the resulting equations.
r = 0 or The roots are 0 and 14. Check by substituting 0 and
14 in for r in the original equation.
The roots are 0 and
. Check by substituting 0 and
in for p in the original equation.
So, the solutions are 0 and 14.
So, the solutions are 0 and
.
2
12. r = 14r
SOLUTION: Rewrite the equation so one side has 0 and the other
side is in factor form. Next, apply the Zero Product
Property by setting each factor equal to 0. Solve
each of the resulting equations.
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r = 0 or Page 3